Fuel Cell Flow Channels and Flow Fields

ABSTRACT

A fuel cell anode flow field includes at least one flow channel with a cross-sectional area that varies along at least a portion of its length. In some embodiments, the channel width decreases along at least a portion of the channel length according to a natural exponential function. This type of anode flow field can improve performance, reduce fuel consumption and/or reduce detrimental effects such as carbon corrosion and catalyst degradation, thereby improving fuel cell longevity and durability. When operating the fuel cell on either a substantially pure or a dilute fuel stream, this type of anode flow field can provide more uniform current density. These flow channels can be incorporated into reactant flow field plates, fuel cells and fuel cell stacks.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Application No.PCT/CA2013/050627 having a filing date of Aug. 14, 2013 entitled “FuelCell Flow Channels and Flow Fields”, which is related to and claimpriority benefits from U.S. Provisional Patent Application Ser. No.61/683,156 filed Aug. 14, 2012, entitled “Fuel Cell Components, Stacksand Systems Based on a Cylindrical Fuel Cell Stack Architecture”, U.S.Provisional Patent Application Ser. No. 61/712,010 filed Oct. 10, 2012,entitled “Fuel Cell Anode Flow Field” and U.S. Provisional PatentApplication Ser. No. 61/712,236 filed Oct. 10, 2012 entitled “Fuel CellFlow Fields Incorporating Improved Flow Channels for EnhancedPerformance”. This application also claims priority benefits from the'156, '236, and '010 applications.

The PCT/CA2013/050627 international application, 61/683,156 provisionalapplication, 61/712,010 provisional application, and 61/712,236provisional application are each hereby incorporated by reference hereinin their entireties.

FIELD OF THE INVENTION

This present invention relates generally to fuel cells, and inparticular to flow field designs and flow field plates for fuel cells.

BACKGROUND OF THE INVENTION

In typical polymer electrolyte membrane (PEM) fuel cells, a membraneelectrode assembly (MEA) is disposed between two electrically conductiveseparator plates. Oxidant and fuel flow fields provide means fordirecting the oxidant and fuel to respective electrocatalyst layers ofthe MEA, specifically, to an anode on the fuel side and to a cathode onthe oxidant side of the MEA. A typical reactant fluid flow field has atleast one channel through which a reactant stream flows. The fluid flowfield is typically integrated with the separator plate by locating aplurality of open-faced channels on one or both faces of the separatorplate. The open-faced channels face an electrode, where the reactantsare electrochemically reacted. Typically more reactant is supplied tothe electrodes than is actually consumed by the electrochemicalreactions in the fuel cell. Stoichiometry (or stoichiometry ratio) canbe defined as the molar flow rate of a reactant supplied to a fuel celldivided by the molar flow rate of reactant consumed in the fuel cell;reactant stoichiometry is the inverse of reactant utilization.

In a single cell arrangement, separator plates are provided on each ofthe anode and cathode sides. The plates act as current collectors andprovide structural support for the electrodes. In a fuel cell stack,often bipolar plates, having reactant flow fields on both sides, areinterleaved with MEAs.

In conventional fuel cell flow fields, the reactant flow channels have aconstant cross-sectional area and shape along their length. Typicallythe channels are square or rectangular in cross-section. However, fuelcells where the cross-sectional area of flow channels varies along theirlength are known. For example, Applicant's issued U.S. Pat. No.6,686,082 and U.S. Patent Application Publication No. US2006/0234107(each of which is hereby incorporated by reference herein in itsentirety) describe fuel cell flow field plates with a trapezoidal form,in which the flow channels are rectangular in cross-section and have across-sectional area that continuously diminishes in the flow direction.In particular, embodiments are described in which the flow channel widthdecreases linearly in the flow direction. Such tapered channels providean increasing in reactant velocity along the channel, and were intendedto provide some of the advantages of serpentine flow channels withoutthe significant pressure drop and the related increase in parasitic loadusually associated with serpentine flow channels. Serpentine flow fieldsprovide higher reactant velocity and improved water removal in thechannels relative to conventional flow fields covering roughly the sameflow field area.

It is also known that it is possible to enhance fuel cell performance byvarying the cross-sectional area of cathode flow channels along theirlength. Fuel cells generally operate on a dilute oxidant stream, namelyair, at the cathode. As the air flows along the cathode flow channel(s),the oxygen content in the air stream tends to be depleted and the airpressure tends to drop. This can result in reduced performance anduneven current density in the fuel cell. Applicant's issued U.S. Pat.No. 7,838,169 (which is incorporated herein by reference in itsentirety) describes improved cathode flow field channels, with a moresophisticated variation in channel cross-section, which can be used toachieve substantially constant oxygen availability at the cathode.Embodiments are described in which the cross-sectional area of thechannels varies along the length of the channels such that oxygenavailability is kept substantially constant for a given channel lengthand air stoichiometry. In some embodiments the channel width decreasesin the oxidant flow direction according to an exponential function. Bymaintaining substantially constant oxygen availability along thechannel, use of such cathode flow channels has been shown to provideimproved uniformity of current density and to enhance fuel cellperformance.

There are a number of factors that can lead to irreversible performancelosses and/or loss of electrochemical surface area during prolongedoperation in PEM fuel cells. The losses are mainly the result ofcatalyst layer degradation including platinum metal dissolution andcorrosion of carbon supports. Carbon corrosion can be caused by cellreversal which, in turn, can be a result of uneven reactant distributionand/or fuel starvation in regions of the anode. Platinum dissolution canbe caused by high potentials at the cathode or anode which can occurwhen there is heterogeneous current distribution. Individually orcoupled together, these degradation rates can be significant and requiremitigation for long term stable operation. Operating a fuel cell withuniform current density can reduce carbon corrosion and platinumdissolution, both of which are detrimental to fuel cell performance,longevity and durability. It can be postulated that achieving moreuniform current density will reduce fuel cell degradation rates andthereby improve fuel cell lifetime. Furthermore, increasing velocitiesdown the channel can reduce the residence time of hydrogen/air frontsduring air purge cycles at the anode during fuel cell start-stopsequences, leading to reduced carbon corrosion rates and improveddurability.

The flow field channels described in the '169 patent were originallydeveloped for and applied at the fuel cell cathode, and were notexpected to provide particular benefits at the anode, at least in partbecause fuel cell operation on substantially pure hydrogen does notresult in substantial mass transport losses due to high concentrationand the high diffusivity of the hydrogen molecule. However, Applicantshave now determined that such flow field channels can be modified foruse at the anode to enhance fuel cell performance when the fuel cell isoperating on a dilute fuel, and to provide performance benefits evenwhen the fuel cell is operating on a substantially pure fuel.

Often a substantially pure fuel stream (such as hydrogen) is used at thefuel cell anode, and the issue of reactant depletion and reactantavailability along the anode flow channels is not the same as with airat the cathode. Usually, for operation on a substantially pure fuel, theanode flow field is “dead-ended”, and the fuel cell or fuel cell stackis fitted with a bleed- or purge-valve for removing impurities,contaminants and/or water that tends to accumulate in the downstreamportion of the anode flow channels as fuel is consumed during operationof the fuel cell. This accumulation of “inerts” can result in unevencurrent density, resulting in reduced fuel cell performance.Furthermore, accumulation of water in the anode flow channels can causeother problems including blocking fuel access to the anode catalystsleading to a fuel starvation condition that has been linked to bothcarbon corrosion and noble metal catalyst dissolution. Applicants havedetermined that flow field channels similar to those described in the'169 patent can be modified for use at the anode to reduce some of thesedetrimental effects at the anode, and enhance fuel cell performance evenon a substantially pure fuel. Such channels can provide an increase inthe velocity of the fuel during its passage along the channel. It isbelieved that this can improve fuel utilization, as increasing the flowvelocity on the anode can provide a higher fuel availability leading toa leveling of the current density at lower flow rates. This can reducefuel consumption for a given power output. Furthermore, if the fuel cellis operating on a dilute fuel stream (such as a reformate stream whichcontains hydrogen, or aqueous methanol), as the fuel stream flows alongthe flow channels, the hydrogen content in the stream tends to bedepleted and the fuel stream pressure tends to drop. Both of these canresult reduced fuel cell performance. The anode flow field channelsdescribed herein can be used to compensate for the depletion of fuel,achieving substantially constant fuel availability on a dilute fuel, andthereby providing more uniform current density.

In addition to their modification for use at the anode, furtherimprovements and variations on the flow field channels and flow fieldsdescribed in the '169 patent have been made and are described herein. Inparticular, embodiments in which such flow channels can be incorporatedor retrofit into conventional rectangular fuel cell geometries at theanode and/or cathode (rather than trapezoidal fuel cells) with highutilization of the fuel cell active area and efficient use of MEA andplate materials are described. Embodiments are also described in whichthe characteristics of the channel vary as a function of distance alongthe channel in accordance with the same or similar principles as in the'169 patent and as described herein, but along only a portion of thechannel length. Further embodiments are described in which thecharacteristics of the channel vary as a function of distance along thechannel in accordance with the same or similar principles, but in astepwise or discontinuous manner. Such embodiments can be used toachieve at least some of the performance benefits described above, andcan also provide options for improved flow fields that are easier tofabricate or to incorporate into rectangular fuel cell plate geometries.

SUMMARY OF THE INVENTION

The above and other benefits are achieved by a fuel cell anode flowfield plate comprising a fuel inlet, a fuel outlet, and at least onechannel formed in a major surface of the plate, the at least one channelhaving a floor and a pair of side walls extending between the floor andthe major surface, the at least one channel having a length that fluidlyinterconnects the fuel inlet and the fuel outlet, the side wallsseparated by a distance defining a channel width, the floor and themajor surface separated by a distance defining a channel depth.

In the foregoing anode flow field plate, the at least one channel has across-sectional area that decreases exponentially along at least aportion of the channel length.

In a preferred embodiment of the foregoing anode flow field plate, thechannel depth is substantially constant and the channel width decreasesexponentially along at least a portion of the channel length.

In another preferred embodiment, the channel cross-sectional areadecreases according to a natural exponential function. The channel widthat a selected lengthwise position of the at least one channel ispreferably proportional to a natural exponential function of theselected lengthwise position. The natural exponential functionpreferably comprises a constant derived from a fuel stoichiometry of thefuel cell. The constant is preferably a natural logarithm of a functionof the fuel stoichiometry.

In another preferred embodiment, the channel width varies as a functionof distance along the portion of the channel length such that:

${W(x)} = {{W(0)}^{{- \frac{x}{L}}{\ln {(\frac{STOICH}{{STOICH} - 1})}}}}$

where W(x) is the channel width at lengthwise position x, x is aselected position along the channel length [m], W(0) is the channelwidth at the fuel inlet, L is the channel length, and STOICH is the fuelstoichiometry of the fuel cell.

In another embodiment, the cross-sectional area is equal to:

${A(x)} = {\left( {1.35 \times 10^{- 14}} \right)C\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{AVAIL}_{H\; 2}(x)}}$

where A(x) is the channel cross-sectional area at lengthwise position x,x is a selected position along the channel length [m], C is the initialconcentration of hydrogen (%), ρ_(fuel) is the fuel stream density[kg/m], I is the entire channel current load [A], I_(d) is the currentdensity [A/m²], Soich is fuel stoichiometry, W(x) is the width ofchannel at position x[m], and AVAIL_(H2)(x) is hydrogen availability atposition x [kg·m/s²].

In another preferred embodiment, the floor and the side walls arepreferably non-orthogonal. The initial concentration of hydrogen (C) ispreferably approximately 100%. The channel cross-sectional areapreferably has a profile that is one of U-shaped, polygonal,semi-circular, varying fillet channel corner, varying chamfer channelcorner, varying side wall slope angle channel, and varying floor bevel.

In another preferred embodiment, the at least one channel is a pluralityof channels.

The above and other benefits are also achieved by a method of operatinga fuel cell to produce electric power, in which the fuel cell comprisesa membrane electrode assembly interposed between a first separator plateand a second separator plate, the membrane electrode assembly comprisingan anode, a cathode, and a proton exchange membrane interposed betweenthe anode and the cathode. The method comprises connecting the fuel cellto an electrical load; directing a fuel stream across the anode via atleast one anode flow channel formed in a major surface of the firstseparator plate, wherein the at least one anode flow channel has across-sectional area that decreases along its length in the fuel flowdirection; and directing an oxidant stream across the cathode via atleast one cathode flow channel formed in a major surface of the secondseparator plate. The fuel stream is supplied to the at least one anodeflow channel at a fuel stoichiometry such that there is substantiallyuniform current density across the fuel cell.

The above and other benefits are also achieved by a method of operatinga fuel cell to produce electric power, in which the fuel cell comprisesa membrane electrode assembly interposed between a first separator plateand a second separator plate, the membrane electrode assembly comprisingan anode, a cathode, and a proton exchange membrane interposed betweenthe anode and the cathode. The method comprises connecting the fuel cellto an electrical load; directing a fuel stream across the anode via atleast one anode flow channel formed in a major surface of the firstseparator plate, wherein the at least one anode flow channel has across-sectional area that decreases along its length in the fuel flowdirection; directing an oxidant stream across the cathode via at leastone cathode flow channel formed in a major surface of the secondseparator plate. The fuel stream is supplied to the at least one anodeflow channel at a fuel stoichiometry such that fuel availability atprogressively downstream lengthwise positions along the at least oneanode flow channel is kept substantially constant.

In the foregoing methods, the width of the at least one anode flowchannel preferably decreases exponentially in the fuel flow direction.The fuel stream can comprise hydrogen. The fuel stream can also comprisesubstantially pure hydrogen. The fuel stream can also comprise methanolsuch that the fuel cell is a direct methanol fuel cell. The at least onecathode flow channel preferably has a cross-sectional area thatdecreases along its length in the oxidant flow direction, and theoxidant stream is supplied to the at least one cathode flow channel atan oxidant stoichiometry such that oxidant availability at progressivelydownstream lengthwise positions along the at least one cathode flowchannel is kept substantially constant. The at least one anode flowchannel can be a plurality of anode flow channels.

The above and other benefits are also achieved by a fuel cell anode flowfield plate comprising: a reactant inlet; a reactant outlet; and atleast one channel formed in a major surface of the plate, the at leastone channel having a floor and a pair of side walls extending betweenthe floor and the major surface, the at least one channel having alength that fluidly interconnects the reactant inlet and the reactantoutlet, the side walls separated by a distance defining a channel width,the floor and the major surface separated by a distance defining achannel depth. The at least one channel extends in a meandering pathbetween the reactant inlet and the reactant outlet and wherein the atleast one channel has a cross-sectional area that decreasesexponentially along at least a portion of the channel length.

In a preferred embodiment of the foregoing anode flow field plate, thechannel depth is substantially constant and the channel width decreasesexponentially along at least a portion of the channel length. The atleast one channel preferably extends in a serpentine path between thereactant inlet and the reactant outlet, and the channel width decreasesexponentially between the reactant inlet and the reactant outlet. The atleast one channel can also extend in a sinusoidal path between thereactant inlet and the reactant outlet, and the channel width decreasesexponentially between the reactant inlet and the reactant outlet. The atleast one channel can be a plurality of channels. The plurality ofchannels is preferably arranged in a nested configuration and defines aflow field area, preferably a rectangular flow field area.

The above and other benefits are also achieved by a fuel cell anode flowfield plate comprising: a reactant inlet; a reactant outlet; and atleast one channel formed in a major surface of the plate, the at leastone channel having a floor and a pair of side walls extending betweenthe floor and the major surface, the at least one channel having alength that fluidly interconnects the reactant inlet and the reactantoutlet, the side walls separated by a distance defining a channel width,the floor and the major surface separated by a distance defining achannel depth. The at least one channel has a cross-sectional area thatis substantially constant along a first portion of the channel lengthand that decreases exponentially along a second portion of the channellength.

In a preferred embodiment of the foregoing anode flow field plate,channel depth is substantially constant and the channel width decreasesalong the second portion of the channel length. The channel width ispreferably substantially constant and the channel depth preferablydecreases exponentially along the second portion of the channel length.The channel portion having an exponentially decreasing cross-sectionalarea is preferably proximal the reactant inlet and the channel portionhaving a substantially constant cross-sectional area is proximal thereactant outlet. The channel portion having a substantially constantcross-sectional area is also preferably proximal the reactant inlet andthe channel portion preferably has an exponentially decreasingcross-sectional area that is proximal the reactant outlet.

In another preferred embodiment, the plate has a substantially circularmajor planar surface, the reactant outlet is centrally disposed on theplate, and the reactant inlet is disposed at the circumferential edge ofthe plate.

In another preferred embodiment, the at least one channel is a pluralityof channels. The at least one channel preferably extends in a meanderingpath between the reactant inlet and the reactant outlet. The at leastone channel preferably extends in a serpentine path along at least aportion of the channel length. The at least one channel can also extendin a sinusoidal path along at least a portion of the channel length. Theat least one channel can be a plurality of channels. The plurality ofchannels is preferably arranged in a nested configuration and defines aflow field area, preferably a rectangular flow field area.

The above and other benefits are also achieved by a fuel cell anode flowfield plate comprising fuel cell reactant flow field plate comprising areactant inlet, a reactant outlet, least one channel formed in a majorsurface of the plate, the at least one channel having a floor and a pairof side walls extending between the floor and the major surface, the atleast one channel having a length that fluidly interconnects thereactant inlet and the reactant outlet, the side walls separated by adistance defining a channel width, the floor and the major surfaceseparated by a distance defining a channel depth, and a rib extendinglengthwise within at least a portion of the at least one channel, therib having a top surface, a bottom surface and pair of side wallsinterconnecting the top and bottom surfaces, the rib side wallsseparated by a distance defining a rib width, the top surface and thebottom surface separated by a distance defining a rib depth, the ribside walls configured such that the at least one channel is divided intoa pair of channels having cross-sectional areas that decreaseexponentially along at least a portion of the channel length.

In a preferred embodiment of the foregoing anode flow field plate, therib depth is substantially constant and the rib width increasesexponentially along the channel length. The rib width is preferablysubstantially constant and the rib depth preferably increasesexponentially along the channel length.

The above and other benefits are also achieved by a fuel cell anode flowfield plate comprising: a reactant inlet; a reactant outlet; at leastone channel formed in a major surface of the plate, the at least onechannel having a floor and a pair of side walls extending between thefloor and the major surface, the at least one channel having a lengththat fluidly interconnects the reactant inlet and the reactant outlet,the side walls separated by a distance defining a channel width, thefloor and the major surface separated by a distance defining a channeldepth; and a plurality of rib dots disposed within at least a portion ofthe at least one channel, each of the rib dots partially occluding theat least one channel, the rib dots arranged lengthwise within the atleast one channel such that the at least one channel has across-sectional area for reactant flow that decreases exponentiallyalong the channel portion.

In a preferred embodiment of the foregoing anode flow field plate, atleast one of density and size of the rib dots increases along the atleast one channel.

The above and other benefits are also achieved by a fuel cell anode flowfield plate comprising: a reactant inlet; a reactant outlet; and atleast one channel formed in a major surface of the plate, the at leastone channel having a floor and a pair of side walls extending betweenthe floor and the major surface, the at least one channel having alength that fluidly interconnects the reactant inlet and the reactantoutlet, the side walls separated by a distance defining a channel width,the floor and the major surface separated by a distance defining achannel depth

The at least one channel comprises a series of channel portionsextending lengthwise from the reactant inlet to the reactant outlet,each succeeding channel portion in the series having a cross-sectionalarea that is decreased from that of a preceding channel portion so as toapproximate an exponential decrease in cross-sectional area as thechannel portions are traversed lengthwise from the reactant inlet to thereactant outlet.

In a preferred embodiment of the foregoing anode flow field plate, theat least one channel extends in a meandering path between the reactantinlet and the reactant outlet. The at least one channel preferablyextends in a serpentine path along at least a portion of the channellength. The at least one channel can also extend in a sinusoidal pathalong at least a portion of the channel length. The at least one channelcan be a plurality of channels formed in the plate major surface. Theplurality of channels is preferably arranged in a nested configurationand defines a flow field area, preferably a rectangular flow field area.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a simplified representation of an anode flow field platecomprising a flow channel that decreases in depth, with constant width,along its length.

FIG. 1B is a simplified representation of an anode flow field platecomprising a flow channel that decreases exponentially in width, withconstant depth, along its length.

FIG. 2 shows a trapezoidal anode flow field plate comprising multipleflow channels that decrease exponentially in width along their length.

FIG. 3 is a simplified representation showing an example of how aserpentine flow channel, in which the channel width varies, can beapplied to a rectangular flow field plate.

FIG. 4A is a simplified representation showing an example of how a wavyflow channel, in which the channel width varies, can be applied to arectangular flow field plate.

FIG. 4B is a simplified representation showing an example of howmultiple wavy flow channels can be nested on a rectangular flow fieldplate.

FIG. 5A (prior art) shows a square flow field plate comprising aconventional serpentine flow field with 3 flow channels extendingbetween a supply manifold opening and a discharge manifold opening.

FIG. 5B shows a similar serpentine flow field to FIG. 5A, but where thewidth of each serpentine flow channel decreases exponentially along itslength.

FIG. 6A is a simplified representation of a flow field plate comprisinga flow channel that decreases exponentially in width for a first portionof the channel length and is then constant for a second portion of thechannel

FIG. 6B is a simplified representation of a flow field plate comprisinga flow channel that is constant in width a first portion of the channellength and decreases exponentially for a second portion of the channellength.

FIG. 7A is a simplified representation showing how 3 flow channels ofthe type shown in FIG. 6B can be arranged radially on an annular flowfield plate.

FIG. 7B is a simplified representation showing how multiple flowchannels of the type shown in FIG. 6B can be arranged in a radial arrayon an annular flow field plate.

FIG. 8 is a simplified representation of a flow field plate comprisingtwo flow channels that are initially serpentine with constant width, andthen the channel width decreases exponentially for a second portion ofthe channel length.

FIG. 9 is a simplified representation of a flow field plate comprising aflow channel in which the channel depth is constant along a firstportion of the channel length and then decreases along second a portionof the channel length.

FIG. 10A (prior art) shows a rectangular flow field plate comprising amulti-channel serpentine flow field extending between a supply and adischarge manifold opening.

FIG. 10B shows a modification to the flow field plate of FIG. 10A, inwhich the width of each channel decreases exponentially along a middleportion of the length of each channel.

FIG. 11 is a simplified representation of a flow field plate comprisinga substantially rectangular flow channel having a central rib withexponentially curved side walls.

FIG. 12 is a simplified representation of a flow field plate comprisinga flow channel that has a conventional rectangular cross-section at oneend and is gradually filleted to reduce its cross-section towards theother end, in the flow direction.

FIG. 13 is a simplified representation of a flow field plate comprisinga rectangular flow channel incorporating rib dots, where density of therib dots increases in the flow direction.

FIG. 14 is a simplified representation of a flow field plate comprisinga wavy flow channel incorporating rib dots, where density of the ribdots increases in the flow direction.

FIG. 15 is a simplified representation illustrating an example where theflow channel width decreases in a stepwise, non-linear fashion in theflow direction.

FIG. 16 is a simplified representation illustrating another examplewhere the flow channel width decreases in a stepwise, non-linear fashionin the flow direction.

FIG. 17 is a graphical representation illustrating how stepwise ordiscrete changes in channel width can be used to approximate e-flow.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT(S) Anode Flow Channels—forFuel Cell Operation on Pure or Dilute Fuel

According to one embodiment, an anode flow field channel for a PEM fuelcell is designed for maintaining substantially constant fuelavailability for the fuel cell electrochemical reaction along at least aportion of the length of the channel, for a given channel length andfuel stoichiometry, when the fuel cell is operating on either a pure ora dilute fuel stream.

We theorize that fuel availability is proportionate to fuel cellperformance, and that uniform fuel availability promotes uniform currentdensity, which is desirable for efficient fuel cell operation andimproved performance. In the equations and description below, the fuelreferred to is hydrogen, although the description would be applicable toother fuels such as methanol (although the value of the constant wouldchange).

Hydrogen availability is a function of hydrogen mass flow and velocity,and is defined as follows:

$\begin{matrix}{\mspace{79mu} {{{AVAIL}_{H\; 2}(x)} = {{{\overset{.}{m}}_{H_{2}}(x)}{v(x)}}}} & \left( {1\; a} \right) \\{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{A(x)}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}} & \left( {1\; b} \right)\end{matrix}$

wherein,

-   -   AVAIL_(H2)(x) Hydrogen availability at position x [kg·m/s²]    -   {dot over (m)}_(H2)(x)=Mass flow rate of hydrogen at position x        [kg/s]    -   ν(x)=Velocity of flow at position x [m/s]    -   ρ_(fuel)=Fuel stream density [kg/m³]    -   I_(d)=Current density (constant) [A/m²]    -   I=Entire channel current load [A]    -   Stoich=Fuel stoichiometry    -   W(x)=Width of channel at position x [m]    -   A(x)=Cross-sectional area of channel at position x [m²]    -   C=Initial concentration of hydrogen (%)

Assumptions.

To derive equation (1b), the following assumptions were made:

-   -   1. Uniform current density: an objective is to provide an anode        flow channel that can achieve or approach uniform current        density;    -   2. Single phase stale (gas form): to reduce thermodynamic        complexity, liquid water produced by the fuel cell reaction is        considered to be the only fluid in liquid form; all other masses        are considered to be in gas form;    -   3. Evenly distributed hydrogen concentration, velocity, and mass        flow across flow section: complex flow patterns are not        considered in the interest of reducing mass flow complexity;    -   4. Reaction is considered to be local to the flow channel only:        the model does not consider above-rib activity (namely, in the        region between channels where the MEA is in contact with plate,        and is not directly exposed to fuel flowing in the flow        channel);    -   5. Steady state system: the reaction and flows are considered to        be steady state, or unchanging.

H2 Availability Equation Derivation.

Derivation of equation (1b) from equation (1a) is described as follows:

Definition of additional variables used in the derivation:

-   -   x=Position along channel length [m]    -   {dot over (m)}_(H) _(2 consumed) (x)=Mass flow rate of hydrogen        consumed up to position x [kg/s]    -   {dot over (V)}_(fuel)(x)=Volumetric flow rate of fuel stream at        position x [SLPM]    -   I_(acc)(x)=Accumulated current up to position x [A]        As noted above, hydrogen availability is defined as the hydrogen        mass flow rate by velocity [kg·m/s²]:

AVAIL_(H2)(x)={dot over (m)} _(H) ₂ (x)ν(x)  (1a)

In the anode flow channel, hydrogen is consumed as the fuel stream movesalong the flow channel. The mass flow rate of hydrogen at a givenposition x along the channel is:

H ₂ mass flow at x=H ₂ mass flow at inlet−H ₂ mass flow consumed to x:

{dot over (m)} _(H) ₂ (x)={dot over (m)} _(H) ₂ (0)−{dot over (m)} _(H)_(2 Consumed) (x)

-   -   Where {dot over (m)}_(H) ₂ (0)=(0.16×10⁻⁷)(C)ρ_(fuel)·I·Stoich        [kg/s]    -   Where {dot over (m)}_(H) _(2 Consumed)        (x)=(1.16×⁻⁷)(C)ρ_(fuel)·I_(acc)(x) [kg/s]

{dot over (m)} _(H) ₂ (x)=(1.16×10⁻⁷)(C)ρ_(fuel)((I·Stoich)−(x))[kg/s]  (2a)

These equations are based on a well-known empirically derived fuel cellreaction fundamental principle: Hydrogen flow [SLPM]=0.006965×fuelstoichiometry (Stoich)×current load (I). The value 1.16×10⁷ (unitsm³/A·s) is obtained by converting 0.006965 [SLPM] to [m³/s].

The velocity of the fuel stream at a given position x along the channelis:

$\begin{matrix}{{{{Velocity}\mspace{14mu} {at}\mspace{14mu} x} = {{Fuel}\mspace{14mu} {stream}\mspace{14mu} {volumetric}{\mspace{11mu} \;}{flow}\mspace{14mu} {rate}\mspace{14mu} {at}\mspace{14mu} {s/{Flow}}\mspace{14mu} {area}\mspace{14mu} {at}\mspace{14mu} x}}\mspace{20mu} {{v(x)} = \frac{{\overset{.}{V}}_{fuel}(x)}{A(x)}}\mspace{20mu} {{v(x)} = {\frac{\left( {1.16 \times 10^{- 7}} \right){I \cdot {Stoich}}}{A(x)}\mspace{14mu}\left\lbrack {m\text{/}s} \right\rbrack}}} & \left( {2\; b} \right)\end{matrix}$

Combining equations (2a) and (2b) then gives:

$\begin{matrix}{{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{acc}(x)}} \right)}\left( {I \cdot {Stoich}} \right)}{A(x)}\mspace{14mu}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}}\mspace{20mu} {{{Where}\mspace{14mu} {I_{acc}(x)}} = {I_{d}{\int_{0}^{x}{{W(x)}\ {{x\mspace{14mu}\lbrack A\rbrack}}}}}}{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{A(x)}\mspace{14mu}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}}} & \left( {1\; b} \right)\end{matrix}$

Equation (1b) shows that increasing the hydrogen availability can beachieved by:

-   -   Increasing current density (I_(d))    -   Increasing fuel stoichiometry (Stoich)    -   Increasing in channel length (L)    -   Increasing average channel width ( W)    -   Increasing fuel stream density (ρ_(fuel))    -   Decreasing channel depth (D)

As previously discussed, it is desirable to manufacture a fuel cell thatcan achieve substantially uniform current density in operation. Assumingthat uniform current density can be achieved by maintaining uniform fueland oxygen availability along the length (x) of the anode and cathodeflow channels respectively, equation (1b) shows that holding hydrogenavailability constant along x requires changes in flow area. The flowarea A(x) for each position along the channel length can be determinedby solving equation (1b) for A(x) as shown in equation (7) below. For arectangular flow channel cross-section (namely, channel with a straightfloor and side walls), the channel width and depth can be determined atany given lengthwise position x in the channel by defining area A(x) asthe product of width W(x) and depth D(x), then changing the channelwidth or depth (W or D) along channel length x:

$\begin{matrix}{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{D(x)}{W(x)}}\mspace{14mu}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}} & (3)\end{matrix}$

Anode Flow Channel Having Varied Depth Profile

An anode flow channel can be manufactured with a constant width and avarying depth profile to achieve constant hydrogen availability. Such achannel profile is calculated as follows:

Using the hydrogen availability equation as previously derived inequation (3):

$\begin{matrix}{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{D(x)}{W(x)}}\mspace{14mu}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}} & (3)\end{matrix}$

and solving for channel depth D)(x):

${D(x)} = {\left( {1.35 \times 10^{- 14}} \right)C\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{{AVAIL}_{H\; 2}(x)}{W(x)}}}$

Assuming constant hydrogen availability Avail_(H2) and channel width W,the following equation 4 is obtained:

$\begin{matrix}{\mspace{79mu} {{{{{w{here}}\mspace{14mu} {\int_{0}^{x}{{W(x)}\ {x}}}} = {W \cdot x}}\mspace{79mu} {{{where}\mspace{14mu} I} = {I_{d} \cdot W \cdot L}}{{D(x)} = {\left( {1.35 \times 10^{- 14}} \right)C\frac{{\rho_{fuel}\left( {\left( {I_{d} \cdot W \cdot L \cdot {Stoich}} \right) - \left( {I_{d} \cdot W \cdot x} \right)} \right)}\left( {I_{d} \cdot W \cdot L \cdot {Stoich}} \right)}{{AVAIL}_{H\; 2} \cdot W}}}{{D(x)} = {\frac{\left( {1.35 \times 10^{- 14}} \right){C \cdot \rho_{fuel} \cdot {Stoich} \cdot L \cdot I_{D}^{2} \cdot W}}{{AVAIL}_{H\; 2}}{\left( {{L \cdot {Stoich}} - x} \right)\mspace{14mu}\lbrack m\rbrack}}}}\mspace{20mu} {{D(x)} = {{D(0)}{\left( {1 - \frac{x}{L \cdot {Stoich}}} \right)\mspace{14mu}\lbrack m\rbrack}}}}} & (4)\end{matrix}$

The result is the depth profile is linear to x.

FIG. 1A is a simplified representation of an anode flow field plate 100Acomprising a flow channel 110A that decreases in depth, with constantwidth, along its length. A channel profile can be defined by solving forD(x) in equation 4 at each position (x) along the length of the channel,given a specified operating fuel stoichiometry STOICH and channel lengthL, and assuming a constant channel width. Referring to FIG. 1A, theresulting anode channel 110A extends between fuel supply manifoldopening 120A and discharge manifold opening 130A, and has a linearlydecreasing depth floor 112A from inlet 116A to outlet 118A, withstraight (parallel) side walls 114A.

For the varied depth approach, to increase hydrogen availability alongthe channel requires, ordered in effectiveness, an:

-   -   increase in current density (I_(d));    -   increase in fuel stoichiometry (Stoich);    -   increase in channel length (L);    -   increase in channel width (W);    -   increase in fuel stream density (ρ_(fuel)); or,    -   decrease in average depth ( D)

Anode Flow Channel Having Varied Width Profile

Given the desire to reduce or minimize the thickness of the separatorplates in a fuel cell stack, it is desirable to keep the depth of thechannel shallow. Therefore, instead of varying the depth of the channel,which would require a sufficiently thick plate to accommodate thedeepest part of the channel, it can be preferred to keep the channeldepth constant and to vary just the width of the channel to achieveconstant hydrogen availability along the length of the channel.

Again, the H₂ availability equation (3) is:

$\begin{matrix}{{{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{D(x)}{W(x)}}\mspace{14mu}\left\lbrack {{{kg} \cdot m}\text{/}s^{2}} \right\rbrack}}} & (3)\end{matrix}$

Applying constant hydrogen availability Avail_(H2) and channel depth

  where  I = I_(d) ∫₀^(L)W(x) x${{AVAIL}_{H\; 2}(x)} = {\left( {1.35 \times 10^{- 14}} \right)C\frac{{\rho_{fuel}\begin{pmatrix}{{{{Stoich} \cdot I_{d}}{\int_{0}^{L}{{W(x)}\ {x}}}} -} \\{I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}\end{pmatrix}}\left( {I_{d} \cdot {\int_{0}^{L}{{W(x)}\ {{x} \cdot {Stoich}}}}} \right)}{D \cdot {W(x)}}}$

Solving for W(x), equation (5) is as follows:

$\begin{matrix}{\frac{W(x)}{\begin{pmatrix}{{{{Stoich} \cdot I_{d}}{\int_{0}^{L}{{W(x)}\ {x}}}} -} \\{I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}\end{pmatrix}\left( {I_{d} \cdot {\int_{0}^{L}{{W(x)}\ {{x} \cdot {Stoich}}}}} \right)} = \frac{\rho_{fuel}}{\left( {1.35 \times 10^{- 14}} \right){C \cdot {AVAIL}_{H\; 2} \cdot D}}} & (5)\end{matrix}$

Equation (5) can be simplified to obtain

$\begin{matrix}{{W(x)} = {{W(0)}{^{{- \frac{x}{L}}{\ln {(\frac{STOICH}{{STOICH} - 1})}}}\mspace{14mu}\lbrack m\rbrack}}} & (6)\end{matrix}$

FIG. 1B is a simplified representation of an anode flow field plate 100Bcomprising a flow channel 110B that decreases in width along its length.A channel profile can be defined by solving for W(x) in equation (6) ateach position (x) along the length of the channel, given a specifiedoperating fuel stoichiometry STOICH and channel length L, and assuming aflat channel floor (constant depth). Referring to FIG. 1B, the resultinganode channel 110B extends between fuel supply manifold opening 120B anddischarge manifold opening 130B, and has a constant depth floor 112Bwith convexly curved side walls 114B that converge inwards from inlet tooutlet. The walls 114B converge inwards towards an outlet end 118B withan inlet 116B having the largest width and the channel profiledelineating at a diminishing rate. That is, the channel width decreasesexponentially along the length of the channel from the inlet to theoutlet according to the equation (6). It would be possible for one ofthe side walls to be straight and the other to be convexly curved.

Referring to FIG. 2, multiple channels 210 having the channel profileshown in FIG. 1B can be applied to a separator plate 200, to form ananode flow field 222 extending between fuel supply manifold opening 220and discharge manifold opening 230. The anode flow field 222 is arrayedin a generally trapezoidal geometry to enable separating ribs 224 tohave a relatively even width along their length; it can be seen thatusing a conventional rectangular flow field geometry with narrowing flowchannels would require the ribs to also have a narrowing profile. Such arib profile would result in significant amounts of MEA contacting theribs, resulting in reduced membrane active area and less efficient usageof membrane material. Since MEA material is relatively expensive, it canbe desirable to maximize the MEA active area using a generally even ribwidth. Using a generally trapezoidal flow field geometry also enablesthe flow field 222 to fit onto a trapezoidal separator plate 200, or tofit onto a traditional rectangular separator plate with room to spare onthe separator plate for other components such as manifolding (notshown).

The separator plate 200 includes partial ribs 226 located at the inletregion of each channel 210. The partial ribs 226 serve to reduce thedistance between channel side walls, and serve as a bridging or supportstructure for the adjacent MEA (not shown).

Anode Flow Channel Having Varied Cross-Sectional Area

If alternate techniques are used to generate a constant H₂ availabilityprofile without a rectangular channel cross-section (flat floor,vertical walls), then a new variable W_(R)(x) is introduced intoequation (1(b)). W_(R)(x) is defined as the width of the hydrogenreaction area at a given lengthwise position x along the channel (for arectangular channel cross-section, W_(R)(x)=W(x) as the width of thechannel that is exposed to the adjacent MEA or gas diffusion layer isthe same as the channel width). A(x) is then calculated throughiteration based on channel profile. The resulting equation (7)encompasses various channel cross-sectional flow shapes that maintain aconstant H₂ availability along the channel length. For example,alternative channel cross-sectional profiles can include, but are notlimited to: U-shaped channel, polygonal channel, semi-circular channel,varying fillet channel corner, varying chamfer channel corner, varyingside wall slope angle channel, or varying floor bevel.

$\begin{matrix}{{A(x)} = {\left( {1.35 \times 10^{- 14}} \right)C{\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{AVAIL}_{H\; 2}(x)}\mspace{14mu}\left\lbrack m^{2} \right\rbrack}}} & (7)\end{matrix}$

The preferred anode flow channel dimensions or characteristics based onthe equations set forth above are applicable to operation on pure ordilute fuels as the equations take into account concentration (C).

Improved Reactant Flow Field Designs

As used herein, the terms “e-flow”, “based on e-flow”, “based on thee-flow equations”, “in accordance with e-flow principles”, “e-flowchannels”, and similar phrases are intended to refer to reactant flowchannel dimensions, flow characteristics and/or flow field designs thatare selected based on the equations and description set forth above withrespect to the anode, and in U.S. Pat. No. 7,838,169 with respect to thecathode. Such channels or flow field designs can be incorporated intothe anode and cathode flow field plates or other components of a fuelcell.

Flow fields based on e-flow principles are more likely to be adopted ifthey can be accommodated within conventional flow field plate geometriesand into conventional fuel cell stack architectures (which typicallyhave rectangular flow field plates). Flow channels where the depthprofile changes along the length of the channel (such as shown in FIG.1B) can be accommodated by using the existing flow field design(pattern) and merely altering the depth profile of the channels alongtheir length (keeping the channel width and ribs the same as in theoriginal flow field design). However, plates with channels where thedepth profile changes are generally more challenging to fabricate. Theyalso result in a need for thicker plates, in order to accommodate thedeepest part of the channel, leading to decreased fuel cell stack powerdensity and higher cost.

FIGS. 3-5 show some examples of ways in which flow fields based one-flow where the flow channel width varies, can be applied to arectangular reactant flow field plate. FIG. 3 shows a rectangularreactant flow field plate 300 with a serpentine channel 310 where thechannel width is decreasing exponentially as it zig-zags across theplate between supply manifold opening 320 and discharge manifold opening330. FIG. 4A shows a rectangular reactant flow field plate 400A with awavy channel 410A extending between supply manifold opening 420A anddischarge manifold opening 430A, where the channel width is decreasingexponentially along its length. In FIG. 4A the amplitude of the path ofthe center-line of the flow channel 410A increases as the width of thechannel decreases, so that the channel still occupies most of the widthof the plate 400A. Making the variable width e-flow channel serpentineor wavy, rather than straight, allows the channel to occupy a morerectangular shape making more efficient use of the surface area of theplate. FIGS. 3 and 4A show a single flow channel, however, it isapparent that such channels can be repeated or arrayed across arectangular plate so that a large portion of the plate area can be“active area” (for example, so that a large portion of the plate surfaceis covered in channels, with a large open channel area exposed to theadjacent electrode or MEA). FIG. 4B shows a rectangular reactant flowfield plate 400B with multiple flow channels 410B (like flow channel410A of FIG. 4A repeated) extending between supply manifold opening 420Band discharge manifold opening 430B, arranged so that the channels nesttogether. This example describes a single direction array (x-axis shown)resulting in an overall approximately rectangular active area, andmaintains substantially uniform rib width (channel spacing). Thisdiffers from a radial or arced array pattern resulting from maintainingsubstantially uniform rib width in the straight e-flow channel profileof FIG. 2. FIG. 5A shows a square flow field plate 500A comprising aconventional (prior art) serpentine flow field with three flow channels510A extending between supply manifold opening 520A and dischargemanifold opening 530A. FIG. 5B shows a similar serpentine flow fieldplate 500B, but where the width of each serpentine channel 510Bdecreases exponentially along its length as it extends from supplymanifold opening 520B to discharge manifold opening 530B.

Another approach is to take a radial array of channels of decreasingwidth, such as is shown in FIG. 2, and incorporate a 90° “fan” of suchchannels on a square plate with discharge manifold opening in one corner(where narrower ends of the channels converge) and supply manifoldopening in the opposite corner, with a feed header extending along twosides of the square plate. Similarly a 180° fan of channels could beincorporated on a rectangular plate. Rectangular active area shapes aregenerally preferred for flow field plates (and other fuel cellcomponents), as they generally make more efficient use of bulk sheetmaterials with less waste during manufacturing. It is possible toefficiently “nest” circular or trapezoidal plates onto a rectangularsheet, however there is generally more unused area than with rectangularcut shapes.

Improvements in fuel cell performance can be obtained by incorporatinge-flow along only a portion of the length of the reactant flow channel.The performance improvements are not necessarily as great as if e-flowis employed along the entire channel length, but such flow field designscan in some cases provide most of the benefit, and can allow moreefficient use of the plate area. For example, current density maps ofconventional flow fields, such as those having serpentine or straightflow channels, generally show reasonable uniformity of current densitynear the supply manifold followed by a reduction in current densityfurther downstream. This indicates that e-flow can provide the mostbenefit if used in the latter portion of the channel length, where thecurrent density is more sensitive to reactant availability. However, itis possible to incorporate e-flow into the flow field near the beginningof the channel length followed by a downstream section that hasconventional flow channels. This embodiment can be used to hold thereactant availability substantially constant over an initial portion ofthe fuel cell active area, and allow the downstream “conventional”section to operate as though there was no upstream active area. In thisway the e-flow region could be regarded as a power generating “manifold”for the subsequent conventional flow field.

FIGS. 6-8 show some examples where the flow channel width varies alongjust a portion of the length of the channel. FIG. 6A shows a rectangularreactant flow field plate 600A with a flow channel 610A extendingbetween supply manifold opening 620A and discharge manifold opening630A. Similarly, FIG. 6B shows a rectangular reactant flow field plate600B with a flow channel 610B extending between supply manifold opening620B and discharge manifold opening 630B. In FIG. 6A the flow channelwidth decreases exponentially for a first portion 625A of the channellength (near the supply manifold), and is then constant for a secondportion 635A of the channel length (towards the discharge manifold).Conversely, in FIG. 6B the flow channel width is constant for a firstportion 625B and decreases exponentially for a second portion 635B ofthe channel length.

FIGS. 7A & 7B show how flow channels 710 of the type shown in FIG. 6Bcan be arranged radially on an annular reactant flow field plate 700.FIG. 7A is a partial view showing just a few channels 710, and FIG. 7Bshows a complete flow field.

FIG. 8 shows a reactant flow field plate 800 comprising two flowchannels 810. The channels are initially serpentine with constant widthin portion 825 near the supply manifold opening 820, and then, afterabruptly increasing, the channel width decreases exponentially for asecond portion 835 of the channel length (towards discharge manifoldopening 830). FIG. 9 shows an example of a reactant flow field plate 900comprising a flow channel 910 extending between a supply manifoldopening 920 and a discharge manifold opening 930. The flow channel depthis constant along a first portion 925 of the channel length and thendecreases along a second portion 935 of the length of the channel 910.

In some embodiments, the flow channels can incorporate an e-flow basedvariation in both width and depth along their entire length, or aportion of their length.

FIGS. 10A & 10B illustrate how an existing flow field design can bereadily modified to incorporate e-flow along a portion of the length ofthe flow channels. FIG. 10A (prior art) shows a rectangular flow fieldplate 1000A comprising a fairly complex serpentine flow field withmultiple serpentine channels 1010A extending between a supply and adischarge manifold opening. FIG. 10B shows a modification in which thewidth of each channel 1010B decreases exponentially along a middleportion 1025B of the length of each channel.

It is also possible to take a “conventional” flow channel (for example,a channel with a rectangular and constant cross-sectional shape and areaalong its length) and incorporate a shaped rib, fillet or other featureswithin the volume of the original channel to reduce the channelcross-sectional area in a way that provides at least some of thebenefits of e-flow. FIG. 11 shows an example of a reactant flow fieldplate 1100 with a single flow channel 1110 extending between a supplymanifold opening 1120 and a discharge manifold opening 1130. The channel1110 comprises a central rib 1140 with exponentially curved side walls.The rib splits the flow channel 1110 in two and effectively reduces itswidth gradually along most of its length in accordance with e-flowprinciples. FIGS. 12A and 12B show two different views of anotherexample of a flow field plate 1200 with a single flow channel 1210extending between a supply manifold opening 1220 and a dischargemanifold opening 1230. The channel 1210 is of a conventional rectangularcross-section at one end 1225, and is gradually filleted to reduce itscross-section towards the other end 1235, in accordance with e-flowprinciples.

In the examples described above, the flow channel dimensions vary alongat least a portion of the channel length in a smooth and continuousfashion in accordance with e-flow principles. However, performancebenefits can also be obtained by using reactant flow channels thatincorporate a “discrete approximation” of e-flow. In other words, thecharacteristics of the channel can be varied as a function of distancealong the channel in a stepwise or discontinuous fashion, but where theoverall variation trends the smooth e-flow profile, either influctuations about the calculated profile, or in discrete approximationsof the e-flow profile (so that it is in accordance with e-flow at a“macro” level). This approach can be used to achieve at least some ofthe performance benefits of e-flow, and can provide some options forimproved flow fields that are easier to fabricate or to incorporate intoexisting fuel cell plate geometries. In all cases the outlet, or regionnear the outlet is smaller or more constricted that the inlet or inletregion. In some embodiments, the channels can contain discrete featuresthat obstruct reactant flow, where the density and/or size of thosefeatures increases in the flow direction. An example of a flow fieldplate 1300 where the flow channels incorporate rib dots or raisedcolumns 1350 is shown in FIG. 13. The density of the rib dots 1350 canincrease in the reactant flow direction (indicated by the arrow) inaccordance with the e-flow equations. Such features can be as high asthe channel is deep (so that they touch the adjacent electrode) or canobstruct only part of the channel depth. In the example illustrated inFIG. 13, the “channel” is the entire active area and the rib dots (orother such features that obstruct reactant flow) are distributed acrossthe active area in a varied density array approximating e-flow. In otherexamples, the rib dots or other features can be incorporated into one ormore separate channels. FIG. 14 is a simplified representation of ananode flow field plate 1400 comprising a wavy flow channel 1410incorporating rib dots 1450, where the density of the rib dots increasesin the flow direction (indicated by the arrow).

In other examples, the flow channel dimensions (for example, width ordepth) can decrease in the flow direction in a stepwise fashion. Theincrements by which the dimensions change and the distance between thestep-changes are selected so that the changes in channel dimensions inthe flow direction are consistent with the e-flow equations. In someembodiments the increments by which the channel dimensions change can bethe same along the channel length, and in other embodiments it can varyalong the channel length. Similarly, in some embodiments the distancebetween (or frequency of) the step-changes in channel dimensions can bethe same along the channel length, and in other embodiments it can varyalong the channel length.

FIGS. 15 and 16 illustrate examples where the channel width decreases ina stepwise, non-linear fashion in the flow direction in accordance withthe e-flow equations. FIG. 15 is a simplified representationillustrating an example flow field plate 1500 where the width of flowchannel 1510 decreases in a stepwise, non-linear fashion in the flowdirection between a supply manifold opening 1520 and a dischargemanifold opening 1530. FIG. 16 is a simplified representationillustrating another example flow field plate 1600 where the width offlow channel 1610 decreases in a stepwise, non-linear fashion in theflow direction between a supply manifold opening 1620 and a dischargemanifold opening 1630.

FIG. 17 is a graphical representation 1700 illustrating how stepwise ordiscrete changes in channel width can be used to approximate e-flow. Thesolid line 1710 represents changes in channel width and the dashed line1720 shows a smooth exponential variation in channel width.

In other examples the porosity of the flow channel could vary in acontinuous or stepwise fashion in accordance with e-flow principles.

FIGS. 1A, 1B, 3, 4A, 4B, 6A, 6B, 7A, 7B, 8, 9, 11, 12, 13, 14, 15 and 16are simplified drawings, in which the size of the flow channel and themanifold openings, and e-flow based variations in channelcharacteristics are exaggerated for the purposes of clear illustration.

In all of the above-described embodiments, the flow characteristics ofthe flow channel vary along at least a portion of the channel lengthsubstantially in accordance with the e-flow equations. The variationscan be continuous or discrete. In the latter case, a continuous curvefitted to the discrete changes would be substantially consistent withthe e-flow equations.

Flow channels with characteristics as described herein can be used atthe anode or the cathode or both. Also they can be used for some or allof the fuel cells in a particular fuel cell stack.

The open channel area versus the rib or landing area on a reactant flowfield plate is generally selected to give sufficient electrical contactbetween the plates and the adjacent MEAs for efficient currentcollection, while providing sufficient reactant access to the electrodesof the MEA to support the electrochemical reactions. Using a wider ribarea (between flow channels) improves electrical connectivity andcurrent collection in the fuel cell.

As used herein the “inlet” refers to either the start of the flowchannel where reactant enters the channel, or the start of a regionwhere the channel characteristics vary as a function of channel lengthas described herein; and “outlet” refers to either the downstream end ofthe channel, or the end of a region over which channel characteristicsvary as a function of channel length as described herein.

Fuel cell flow field plates can utilize the reactant flow channels orflow field designs described above. Such plates can be made fromsuitable materials or combination of materials, and can be fabricated bysuitable methods.

Other fuel cell components can also incorporate the flow channels orpassageways as described herein. For example, such channels could beincorporated into the gas diffusion layer, or other components of theunit cell.

Fuel cells and fuel cell stacks can also incorporate the flow fieldplates and/or other components. The reactant flow channels and flowfield designs described herein have been found to be particularlyadvantageous in PEM fuel cells, however they can be applied in othertypes of fuel cells or other electrochemical devices, such aselectrolyzers.

Where a component is referred to above, unless otherwise indicated,reference to that component should be interpreted as including theequivalents of that component and any component which performs thefunction of the described component (namely, that is functionallyequivalent), including components which are not structurally equivalentto the disclosed structure but which perform the function in theillustrated exemplary embodiments.

While particular elements, embodiments and applications of the presentinvention have been shown and described, it will be understood, that theinvention is not limited thereto since modifications can be made withoutdeparting from the scope of the present disclosure, particularly inlight of the foregoing teachings.

What is claimed is:
 1. A fuel cell anode flow field plate comprising:(a) a fuel inlet; (b) a fuel outlet; and (c) a channel formed in a majorsurface of said plate, said channel having a floor and a pair of sidewalls extending between said floor and said major surface, said channelhaving a length that fluidly interconnects said fuel inlet and said fueloutlet, said side walls separated by a distance defining a channelwidth, said floor and said major surface separated by a distancedefining a channel depth, wherein said channel has a cross-sectionalarea that decreases exponentially along a portion of said channellength.
 2. The anode flow field plate of claim 1, wherein said channeldepth is substantially constant and said channel width decreasesexponentially along a portion of said channel length.
 3. The anode flowfield plate of claim 1, wherein said channel cross-sectional areadecreases according to a natural exponential function.
 4. The anode flowfield plate of claim 3, wherein said channel width at a selectedlengthwise position of said channel is proportional to a naturalexponential function of said selected lengthwise position, and saidnatural exponential function comprises a constant derived from a fuelstoichiometry of the fuel cell.
 5. The anode flow field plate of claim1, wherein said channel width varies as a function of distance alongsaid portion of said channel length such that:${W(x)} = {{W(0)}^{{- \frac{x}{L}}{\ln {(\frac{STOICH}{{STOICH} - 1})}}}}$where W(x) is the channel width at lengthwise position x, x is aselected position along the channel length [m], W(0) is the channelwidth at the fuel inlet, L is the channel length, and STOICH is the fuelstoichiometry of the fuel cell.
 6. The anode flow field plate of claim1, wherein said cross-sectional area is equal to:${A(x)} = {\left( {1.35 \times 10^{- 14}} \right)C\frac{{\rho_{fuel}\left( {\left( {I \cdot {Stoich}} \right) - {I_{d}{\int_{0}^{x}{{W(x)}\ {x}}}}} \right)}\left( {I \cdot {Stoich}} \right)}{{AVAIL}_{H\; 2}(x)}}$where A(x) is the channel cross-sectional area at lengthwise position x,x is a selected position along the channel length [m], C is the initialconcentration of hydrogen (%), P_(fuel) is the fuel stream density[kg/m³], I is the entire channel current load [A], I_(d) is the currentdensity [A/m²], Stoich is fuel stoichiometry, W(X) is the width ofchannel at position x [m], and AVAIL_(H2)(x) is hydrogen availability atposition x [kg·m/s²].
 7. The anode flow field plate of claim 6, whereinsaid floor and said side walls are non-orthogonal.
 8. The anode flowfield plate of claim 6, wherein the initial concentration of hydrogen(C) is approximately 100%.
 9. The anode flow field plate of claim 6,wherein said channel cross-sectional area has a profile that is one ofU-shaped, polygonal, semi-circular, varying fillet channel corner,varying chamfer channel corner, varying side wall slope angle channel,and varying floor bevel.
 10. The anode flow field plate of claim 1,wherein said channel is one of a plurality of channels.
 11. The anodeflow field plate of claim 10, wherein said plate is configured to beused in a fuel cell.
 12. The anode flow field plate of claim 10, whereinsaid plate is configured to be used in a plurality of fuel cells,wherein said plurality of fuel cells are utilized in a fuel cell stack.13. A method of operating a fuel cell to produce electric power themethod comprising: (a) connecting said fuel cell to an electrical load,wherein said fuel cell comprises a membrane electrode assemblyinterposed between a first separator plate and a second separator plate,said membrane electrode assembly comprising an anode, a cathode, and aproton exchange membrane interposed between said anode and said cathode;(b) directing a fuel stream across said anode via an anode flow channelformed in a major surface of said first separator plate, wherein saidanode flow channel has a cross-sectional area that decreases along itslength in the fuel flow direction; (c) directing an oxidant streamacross said cathode via a cathode flow channel formed in a major surfaceof said second separator plate, wherein said fuel stream is supplied tosaid anode flow channel at a fuel stoichiometry such that there issubstantially uniform current density across the fuel cell.
 14. A methodof operating a fuel cell to produce electric power said methodcomprising: (a) connecting said fuel cell to an electrical load, whereinsaid fuel cell comprises a membrane electrode assembly interposedbetween a first separator plate and a second separator plate, whereinsaid membrane electrode assembly comprises an anode, a cathode, and aproton exchange membrane interposed between said anode and said cathode;(b) directing a fuel stream across said anode via an anode flow channelformed in a major surface of said first separator plate, wherein saidanode flow channel has a cross-sectional area that decreases along itslength in the fuel flow direction; and (c) directing an oxidant streamacross said cathode via a cathode flow channel formed in a major surfaceof said second separator plate, wherein said fuel stream is supplied tosaid anode flow channel at a fuel stoichiometry such that fuelavailability at progressively downstream lengthwise positions alonganode flow channel is kept substantially constant.
 15. The methodaccording to claim 13 or 14, wherein the width of said anode flowchannel decreases exponentially in the fuel flow direction.
 16. Themethod according to claim 13 or 14, wherein said fuel stream issubstantially pure hydrogen.
 17. The method according to claim 13 or 14,wherein said cathode flow channel has a cross-sectional area thatdecreases along its length in the oxidant flow direction, and saidoxidant stream is supplied to said cathode flow channel at an oxidantstoichiometry such that oxidant availability at progressively downstreamlengthwise positions along said cathode flow channel is keptsubstantially constant.